Chemistry for Engineering Students
Chemistry for Engineering Students
4th Edition
ISBN: 9781337398909
Author: Lawrence S. Brown, Tom Holme
Publisher: Cengage Learning
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Textbook Question
Chapter 9, Problem 9.37PAE

9.37 A calorimeter contained 75.0 g of water at 16.95°C. A 93.3-g sample of iron at 65.58°C was placed in it, giving a final temperature of 19.68°C for the system. Calculate the heat capacity of the calorimeter. Specific heats are 4 . 184J g 1 ° C 1 for H 2 O and 0.444 J g 1 ° C 1 for Fe.

Expert Solution & Answer
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Interpretation Introduction

Interpretation:

Using the information provided, the solutions can be obtained by calculations using suitable formulas.

Concept Introduction:

  • The specific heat is the amount of heat per unit mass required to raise the temperature by one degree Celsius. Formula for heat required is-

     Heat required,Q=c×m×ΔT

    Where

    c = specific heat of the substance

    m = mass of the substance

    ΔT = Temperature difference

  • According to the first law of thermodynamics,

    Qiron = Qcalorimetersystem

    Qcalorimetersystem= Qcalorimeter+Qwater

Answer to Problem 9.37PAE

Solution:

Heat capacity of calorimeter = 5.1025 J g-1 oC-1

Explanation of Solution

Given information:

Mass of water in the calorimeter = 75.0 g

Temperature of water in the calorimeter = 16.95 oC

Mass of sample of iron = 93.3 g

Temperature of sample of iron = 65.58 oC

Final temperature = 19.68 oC

Specific heat capacity of water = 4.184 J g -1 oC-1

Specific heat capacity of iron = 0.444 J g -1 oC-1

According to the thermodynamic equation is-

Qiron = Qcalorimetersystem

Qcalorimetersystem= Qcalorimeter+Qwater

Where

Qiron=Cp×ΔT×m

Cp= Specific heat capacity of iron

ΔT = Temperature difference

m = mass of the iron

Qcalorimeter system=Cp(calorimeter system)×ΔT×m(water)

Cp(water)= Specific heat capacity of water

Specific heat of water = 4.184 J g-1 oC-1

ΔT = Temperature difference

m(water) = mass of the titanium water

Therefore

Qiron =Qcalorimeter  systemQcalorimeter system= Qcalorimeter +QwaterCp×ΔT×m=Cp( calorimeter    system)×ΔT×m(water)0.444×(65.5819.68)×93.3=Cp( calorimeter    system) ×(19.6816.95)×75.0Cp( calorimeter    system)=0.444×(65.5819.68)×93.3(19.6816.95)×75.0Cp( calorimeter    system)=0.444×(45.9)×93.3(2.73)×75.0Cp( calorimeter    system)=1901.4166204.75=9.2865Qcalorimeter system= Qcalorimeter +Qwater9.2865= Qcalorimeter +4.184Qcalorimeter =9.28654.184=5.1025

Heat capacity of calorimeter = 5.1025 J g-1 oC-1

Conclusion

Heat capacity of calorimeter = 5.1025 J g-1 oC-1

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Chapter 9 Solutions

Chemistry for Engineering Students

Ch. 9 - Prob. 9.3PAECh. 9 - Prob. 9.4PAECh. 9 - Prob. 9.5PAECh. 9 - Prob. 9.6PAECh. 9 - Define the term internal energy.Ch. 9 - How fast (in meters per second) must an iron ball...Ch. 9 - What is the kinetic energy of a single molecule of...Ch. 9 - 9.10 The kinetic energy of molecules is often used...Ch. 9 - 9.11 Analyze the units of the quantity...Ch. 9 - 9.12 How many kilojoules are equal to 3.27 L atm...Ch. 9 - Prob. 9.13PAECh. 9 - Prob. 9.14PAECh. 9 - 9.15 Carry out the following conversions of energy...Ch. 9 - 9.16 According to Figure 9.2, the total energy...Ch. 9 - 9.17 If a machine does 4.8103kJ of work after an...Ch. 9 - 9.18 Calculate (a) q when a system does 54J of...Ch. 9 - 9.19 If the algebraic sign of E is negative, in...Ch. 9 - 9.20 State the first law of thermodynamics briefly...Ch. 9 - 9.21 Which type of energy heat or work, is valued...Ch. 9 - 9.12 PV-work occurs when volume changes and...Ch. 9 - 9.23 Which system does not work: (a) E=436J ,...Ch. 9 - 9.29 In which case is heat added to the system:...Ch. 9 - Prob. 9.25PAECh. 9 - 9.26 Gas furnaces have achieved impressive...Ch. 9 - Prob. 9.27PAECh. 9 - 9.28 When an electrical appliance whose power...Ch. 9 - Prob. 9.29PAECh. 9 - 9.30 For the example of shallow water and sandy...Ch. 9 - 9.31 A metal radiator is made from 26.0 kg of...Ch. 9 - 9.32 The material typically used to heat metal...Ch. 9 - 9.33 Copper wires used to transport electrical...Ch. 9 - 9.34 A copper nail and an iron nail of the same...Ch. 9 - 9.35 A piece of titanium metal with a mass of 20.8...Ch. 9 - 9.36 Define the term calibration.Ch. 9 - 9.37 A calorimeter contained 75.0 g of water at...Ch. 9 - 9.38 The energy densities of various types of coal...Ch. 9 - 9.39 How much thermal energy is required to heat...Ch. 9 - Prob. 9.40PAECh. 9 - 9.41 Under what conditions does the enthalpy...Ch. 9 - 9.42 Why is enthalpy generally more useful than...Ch. 9 - Prob. 9.43PAECh. 9 - Prob. 9.44PAECh. 9 - 9.45 What happens to the temperature of a material...Ch. 9 - 9.46 The heat of fusion of pure silicon is 43.4...Ch. 9 - 9.47 If 14.8 kJ of heat is given off when 1.6 g of...Ch. 9 - 9.48 Calculate the energy required to convert 1.70...Ch. 9 - 9.49 Hvap=31.3 kJ/mol for acetone. 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